Power Law - Ten Base with Variable Power to Unknown Exponent Base with Known Power (Level 1)

This math topic focuses on problems involving exponents and specifically the power law. It involves solving for unknown exponents where the base is ten and the powers vary. The problems also include finding these unknown exponents when the exponent base's known power is either squared or cubed. These problems help strengthen skills in manipulating exponent expressions and understanding the properties of exponents, part of a broader unit on exponents that includes negative, fractional, and power law exponents.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponents - Power Law - Ten Base with Variable Power to Unknown Exponent Base with Known Power Worksheet

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Exponents - Power Law - Ten Base with Variable Power to Unknown Exponent Base with Known Power
1
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 4 = (10 to the power of ? ) to the power of 2
a A LaTex expression showing ?=2
b A LaTex expression showing ?=6
c A LaTex expression showing ?=3
d A LaTex expression showing ?=9
e A LaTex expression showing ?=5
f A LaTex expression showing ?=7
2
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 6 = (10 to the power of ? ) to the power of 3
a A LaTex expression showing ?=11
b A LaTex expression showing ?=6
c A LaTex expression showing ?=8
d A LaTex expression showing ?=5
e A LaTex expression showing ?=1
f A LaTex expression showing ?=2
3
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 8 = (10 to the power of ? ) to the power of 2
a A LaTex expression showing ?=4
b A LaTex expression showing ?=11
c A LaTex expression showing ?=10
d A LaTex expression showing ?=13
e A LaTex expression showing ?=2
f A LaTex expression showing ?=3
4
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 12 = (10 to the power of ? ) to the power of 3
a A LaTex expression showing ?=6
b A LaTex expression showing ?=2
c A LaTex expression showing ?=4
d A LaTex expression showing ?=10
e A LaTex expression showing ?=3
f A LaTex expression showing ?=7
5
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 6 = (10 to the power of ? ) to the power of 2
a A LaTex expression showing ?=6
b A LaTex expression showing ?=3
c A LaTex expression showing ?=11
d A LaTex expression showing ?=4
e A LaTex expression showing ?=5
f A LaTex expression showing ?=1
6
Solve for the missing exponent (?)
A LaTex expression showing 10 to the power of 9 = (10 to the power of ? ) to the power of 3
a A LaTex expression showing ?=3
b A LaTex expression showing ?=5
c A LaTex expression showing ?=4
d A LaTex expression showing ?=1
e A LaTex expression showing ?=2
f A LaTex expression showing ?=6